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The role of defects in the design of a space
elevator cable From nanotube to megatube -
Latest research results
Nicola M. Pugno Politecnico di Torino, Italy
2th Int. Conf. on Space Elevator Climber and
Tether Design, December 6-7, 2008, Luxembourg,
Luxembourg
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1. Introduction - Griffith
The father of Fracture Mechanics Alan Arnold
Griffith 1893-1963 The Phenomena of rupture
and flow in solids Philosophical Transactions
of the Royal Society, 221A, 163 (1920).
Deterministic approach
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Weibull (1)
The father of the statistical theory of the
strength of solids Waloddi Weibull 1887-1979 A
statistical theory of the strength of
materials Ingeniörsvetenskapsakademiens
Handlingar 151 (1939).
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1. Stress concentrations and intensifications

Linear Elastic Plate (infinitely large) with an
hole under (remote) traction s.

1. Circular hole stress concentration

(b) Elliptical hole stress concentration
(c) Crack infinite stress concentration, i.e.,
stress intensification
K stress-intensity factor r distance from the
tip
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Maximum stress criterion (2)
Maximum stress material strength
E.g., strength for a plate with a circular hole
1/3 strength for the plate without the hole
independently from the size of the hole!? I
cannot believe it!
Vanishing strength for a plate with a crack!? I
cannot believe it! (PARADOX)
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Griffiths energy balance criterion (2)
Energy release rate fracture energy
Criterion for fracture propagation W total
potential energy W dissipated energy A
crack surface area GC W/A fracture energy of
the material (per unit area) G energy release
rate (per unit area)
Stability (or instable if larger than zero)
E.g., strength for the cracked plate E Young
modulus Improvement not vanishing strength, but
infinite strength for defect free solids!? I
cannot believe it! (PARADOX)
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3. Quantized fracture mechanics (QFM)
Stress intensity factors from Handbooks Very
simple application
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The Griffith case treated with QFM (3)
LEFM can treat only large and sharp cracks QFM
has no restrictions on defect size and shape
LEFM rQ0
This represents the link between concentration
and intensification factors!
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Dynamic quantized fracture mechanics (DQFM, 3)
Quantization not only in space but also in time
(finite time required to generate a fracture
quantum) Kinetic energy T included in the energy
balance
Balance of action quanta
Time quantum
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4. Fracture of nanotubes nanocrack
   
Interatomic distance
QFM formula for blunt cracks with length
from MM
best fit (very reasonable)

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Nanoholes (4)
(m1)
MM
Note in addition that by MM strength reductions
due to one vacancy by factors of 0.81 for (10,0)
and 0.74 for (5,5) nanotubes are again close to
our QFM-based prediction, that yields 0.79 (not
1/3 or 0!).
MM also in good agreement with fully quantum
mechanical calculations
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Nanotensile tests on nanotubes (4)
Stretching of multi-walled carbon nanotubes
between Atomic Force Microscope opposite tips 
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Experiments on Strength of (C) Nanotubes (4)
Measured strength (Ruoffs group) of 64, 45, 43
GPa (against the theoretical (DFT) value of about
100 GPa) Defects!
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Comparison between experiments (4)
(A) Assuming an ideal strength for the
multi-walled carbon nanotubes experimentally
investigated of 93.5GPa, as numerically (MM)
computed, and applying QFM 1. the corresponding
strength for a pinhole m1 defect is 64GPa,
against the measured value of 63GPa, 2. for an
m2 defect is 45GPa, against the measured value
of 43 GPa, 3. for an m3 defect is 39 GPa, as
the measured value, and so on Does a strength
quantization exist? (B) For m tending to
infinity (large holes) the strength reduction is
predicted by QFM of a factor 1/3.36 (close to the
classical 1/3!) (C) In addition note that, also
with an exceptionally small defect -a single
missing atom- a strength reduction by a factor of
20 is expected!
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Ordine del Giorno
Is the strength quantized? (4)
E.g., blunt cracks
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Experiments on ideal strength (4)
Thus, the strength is quantized as a
consequence of the quantization of the defect
size!
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Nanoscale Weibull Statistics (NWS, 5)
Weibull distribution for the strength of
solidsprobability of failure for a specimen of
volume V under tension s
Number of critical defects assumed to be
proportional to the volume V of the specimen
material constants (m Weibulls modulus)
Alternatively, V is substituted by the surface S
of the specimen (for surface predominant defects)
In contrast At nanoscale nearly defect free
structures! We substitute V with a fixed number
n of defect (e.g., n1)
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Application to experimental data on nanotubes (5)
n1 Thus, for nanotubes m around 3
Again, it seems that few defects were responsible
for fracture of that nanotubes
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6. The Nanotube-based space elevator megacable
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Multiscale simulations (5)
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Strength of nanotube-based megacable (5)
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Size-effect (5)
Strength of the megacable? Multiscale approach
10GPa Holes in the cables 30GPa Cracks lt30GPa
Thermodynamic limit 45GPa , not 100GPa
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Elasticity of defective Nanotubes (6)
The increment in compliance could result in a
dynamic instability of the megacable
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Nanobiocomposites (7)

• Fundamental roles of
• Tough soft matrix, (ii) Strong hard inclusions
  and (iii) hierarchy,
• for activating toughening mechanisms at all the
  size-scales

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Example of bio-inspired nanomaterial (7)
Super-nanotubes as hierarchical fiber
reinforcements
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Example of bio-inspired nanomaterial (7)
Toughening mechanism fibre pull-out
N-opt2, to optimize the material with respect to
both strength and toughness, as Nature does in
nacre
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Optimizing Nano-composites (7)
Optimization maps. Iso-hardness lines are drawn
in blue and iso-toughness lines in red. Numbers
along the curves indicate hardness and fracture
toughness increments (of a PCD material).
Theory fitted to experiments.
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Nano-armors (7)
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Conclusions
All models are wrong, but some are useful
(George Box) is valid also in the context of the
space elevator cable design! I would like to
thank Drs. M. Klettner and B. Edwards for the
kind invitation The European Spaceward
Association, for supporting my visit here you
for your attention http//staff.polito.it/nicola.
pugno/ nicola.pugno_at_polito.it
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Main References
N. Pugno, On the strength of the nanotube-based
space elevator cable from nanomechanics to
megamechanics. J. OF PHYSICS -CONDENSED MATTER,
(2006) 18, S1971-1990. N. Pugno. The role of
defects in the design of the space elevator
cable from nanotube to megatube. ACTA MATERIALIA
(2007), 55, 5269-5279. N. Pugno, Space Elevator
out of order?. NANO TODAY (2007), 2, 44-47. N.
Pugno, F. Bosia, A. Carpinteri, Multiscale
stochastic simulations for tensile testing of
nanotube-based macroscopic cables. SMALL (2008),
4/8, 1044-1052. N. Pugno, M. Schwarzbart, A.
Steindl, H. Troger, On the stability of the track
of the space elevator. ACTA ASTRONAUTICA (2008).
In Print. A. Carpinteri, N. Pugno, Are the
scaling laws on strength of solids related to
mechanics or to geometry? NATURE MATERIALS, June
(2005), 4, 421-423. N. Pugno, R. Ruoff, Quantized
Fracture Mechanics, PHILOSOPHICAL MAGAZINE
(2004), 84/27, 2829-2845. N. Pugno, Dynamic
Quantized Fracture Mechanics. INT. J. OF FRACTURE
(2006), 140, 159-168. N. Pugno, New Quantized
Failure Criteria Application To Nanotubes And
Nanowires. INT. J. OF FRACTURE (2006), 141,
311-323. N. Pugno, R. Ruoff, Nanoscale Weibull
statistics. J. OF APPLIED PHYSICS (2006), 99,
024301/1-4. N. Pugno, R. Ruoff, Nanoscale
Weibull Statistics for nanofibers and nanotubes.
J. OF AEROSPACE ENGINEERING (2007), 20,
97-101. N. Pugno, Youngs modulus reduction of
defective nanotubes. APPLIED PHYSICS LETTERS
(2007), 90, 043106-1/3 N. Pugno, Mimicking Nacre
With Super-nanotubes For Producing Optimized
Super-composites. NANOTECHNOLOGY (2006), 17,
5480-5484. V.R. Coluci, N. Pugno, S.O. Dantas,
D.S. Galvao, A. Jorio, Determination of the
mechanical properties of super carbon nanotubes
through atomistic simulations. NANOTECHNOLOGY
(2007), 18, 335702 (7pp). N. Pugno, The
strongest matter Einsteinon could be one billion
times stronger than carbon nanotubes. ACTA
ASTRONAUTICA (2008), 63, 687-689.